72.18.1 problem 1

Internal problem ID [14954]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.3 page 424
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 07:25:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)+9*y(t)=cos(t),y(t), singsol=all)
 

\[ y = \sin \left (3 t \right ) c_{2} +\cos \left (3 t \right ) c_{1} +\frac {\cos \left (t \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 68

DSolve[D[y[t],{t,2}]+9*y[t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \cos (3 t) \int _1^t-\frac {1}{3} \cos (K[1]) \sin (3 K[1])dK[1]+\sin (3 t) \int _1^t\frac {1}{3} \cos (K[2]) \cos (3 K[2])dK[2]+c_1 \cos (3 t)+c_2 \sin (3 t) \]